Work out the next term of the
quadratic sequence shown below.
We know that the number pattern, or
sequence, is a quadratic one when the second difference is constant. Let’s begin by calculating the
first difference in our sequence.
The first term in our sequence is
negative one, and the second term is two. To get from negative one to two, we
need to add three. To get from the second term two to
the third term nine, we add seven, as two plus seven is equal to nine. Finally, to get from the third term
nine to the fourth term 20, we add 11. Nine plus 11 equals 20.
We calculate the second difference
of a sequence by finding the difference of the differences. Firstly, we need to find the
difference between plus three and plus seven. This is equal to plus four. Therefore, the first second
difference is add four. To get from plus seven to plus 11,
we also need to add four. Therefore, the second second
difference is also add four. As the second differences are the
same, we know that our sequence is quadratic.
The next second difference will
also be plus four. Adding four to 11 gives us 15. Therefore, the next first
difference will be 15. 20 plus 15 is equal to 35. This means that the next term of
the quadratic sequence is 35. The first differences are plus
three, plus seven, plus 11, plus 15, and so on. They’re increasing by four each
time. This means that the sequence is
negative one, two, nine, 20, and 35. The fifth term in the sequence is